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Mukherjee Fisher Or like a child: they are born not knowing much, and through exposure to life experience, they slowly learn to solve problems in the world. For neural networks, data is the only experience. Here is a simple explanation of what happens during learning with a feedforward neural network, the simplest architecture to explain. Input enters the network. The coefficients, or weights, map that input to a set of guesses the network makes at the end.

## State-of-the-art in artificial neural network applications: A survey

Weighted input results in a guess about what that input is. The network measures that error, and walks the error back over its model, adjusting weights to the extent that they contributed to the error. The three pseudo-mathematical formulas above account for the three key functions of neural networks: scoring input, calculating loss and applying an update to the model — to begin the three-step process over again.

A neural network is a corrective feedback loop, rewarding weights that support its correct guesses, and punishing weights that lead it to err. Despite their biologically inspired name, artificial neural networks are nothing more than math and code, like any other machine-learning algorithm.

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In fact, anyone who understands linear regression , one of first methods you learn in statistics, can understand how a neural net works. In its simplest form, linear regression is expressed as. That simple relation between two variables moving up or down together is a starting point.

## Artificial neural networks

The next step is to imagine multiple linear regression, where you have many input variables producing an output variable. Now, that form of multiple linear regression is happening at every node of a neural network. For each node of a single layer, input from each node of the previous layer is recombined with input from every other node. That is, the inputs are mixed in different proportions, according to their coefficients, which are different leading into each node of the subsequent layer.

In this way, a net tests which combination of input is significant as it tries to reduce error.

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What we are trying to build at each node is a switch like a neuron… that turns on and off, depending on whether or not it should let the signal of the input pass through to affect the ultimate decisions of the network. When you have a switch, you have a classification problem. A binary decision can be expressed by 1 and 0, and logistic regression is a non-linear function that squashes input to translate it to a space between 0 and 1.

The nonlinear transforms at each node are usually s-shaped functions similar to logistic regression. The output of all nodes, each squashed into an s-shaped space between 0 and 1, is then passed as input to the next layer in a feed forward neural network, and so on until the signal reaches the final layer of the net, where decisions are made. Gradient is another word for slope, and slope, in its typical form on an x-y graph, represents how two variables relate to each other: rise over run, the change in money over the change in time, etc.

To put a finer point on it, which weight will produce the least error?

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Which one correctly represents the signals contained in the input data, and translates them to a correct classification? As a neural network learns, it slowly adjusts many weights so that they can map signal to meaning correctly. Each weight is just one factor in a deep network that involves many transforms; the signal of the weight passes through activations and sums over several layers, so we use the chain rule of calculus to march back through the networks activations and outputs and finally arrive at the weight in question, and its relationship to overall error.

That is, given two variables, Error and weight , that are mediated by a third variable, activation , through which the weight is passed, you can calculate how a change in weight affects a change in Error by first calculating how a change in activation affects a change in Error , and how a change in weight affects a change in activation.

The activation function determines the output a node will generate, based upon its input. In Deeplearning4j , the activation function is set at the layer level and applies to all neurons in that layer. Deeplearning4j , one of the major AI frameworks Skymind supports alongside Keras, includes custom layers, activations and loss functions.

On a deep neural network of many layers, the final layer has a particular role. When dealing with labeled input, the output layer classifies each example, applying the most likely label. Each output node produces two possible outcomes, the binary output values 0 or 1, because an input variable either deserves a label or it does not.

## Handbook of Neural Computing Applications - 1st Edition

After all, there is no such thing as a little pregnant. While neural networks working with labeled data produce binary output, the input they receive is often continuous. That is, the signals that the network receives as input will span a range of values and include any number of metrics, depending on the problem it seeks to solve. For example, a recommendation engine has to make a binary decision about whether to serve an ad or not. But the input it bases its decision on could include how much a customer has spent on Amazon in the last week, or how often that customer visits the site.

### NEURAL NETWORKS AND DEEP LEARNING: A TEXTBOOK

The mechanism we use to convert continuous signals into binary output is called logistic regression. Skip to main content Skip to navigation Academic Aims This module provides an introduction to the theory and implementation of neural networks, both biological and artificial. Learning Outcomes Students completing the module should be able to demonstrate: an understanding of the principles of Neural Networks and a knowledge of their main areas of application; the ability to design, implement and analyse the behaviour of simple neural networks.

Content Introduction: history of neural computing; relationship to Artificial Intelligence.